The hosts, who still have to travel to Italy and England, lie fourth in the table behind third-placed Wales, who next host champions Ireland on March 14.
"We were written off by a lot of people (after a 21-16 home defeat against England), and now we're back in contention," Wales coach Warren Gatland told a news conference.
"In terms of performance we were tough at the breakdown, we made things difficult for them. The better team deserved to win."
The visitors scored through Leigh Halfpenny's boot and Dan Biggar's try, while France's points came from Brice Dulin's try and the kicking of Camille Lopez, who otherwise struggled.
"When your kicking success rate is 50 percent in an international game, it's tough to win," said France coach Philippe Saint-Andre, who was testing his 15th starting halfback pairing since taking charge after the 2011 World Cup, lining up Morgan Parra alongside Lopez.
In a game featuring two teams who have been struggling to play with width, the kickers took centre stage as Lopez cancelled out Halfpenny's early penalty.
After Lopez missed a long-range penalty, Halfpenny kicked Wales ahead after France once again lacked discipline in a ruck.
Les Bleus had a try disallowed six minutes before the break after Lopez's pass to Yoann Huget on the right flank was ruled to be forward.
Lopez's ordeal continued as he missed his second penalty on the stroke of halftime. Parra could not do better early in the second half, his penalty bouncing off the post and out.
Lopez eventually levelled with a routine 23-metre penalty in front of the posts, but the advantage did not last long as France were penalised again for coming in at the side.
CLEVER FLICK
A clinical kicker, Halfpenny made it 9-6 in front of an apathetic Stade de France crowd.
Saint-Andre then made four changes with the entire front row swapping and Sebastien Tillous-Bord coming in for Parra at scrumhalf.
On the hour, Jamie Roberts powered his way through the middle and found Dan Lydiate, whose clever flick went to Biggar for the flyhalf to dive in by the corner and give Wales an eight-point lead.
Halfpenny converted another penalty to make it 17-6 and it spurred France into action, Dulin managing a try in the corner after Les Bleus finally put a few phases together.
Lopez slotted through a tricky conversion to set up a possibly nail-biting finale.
There was always Halfpenny's boot to set things straight though and the fullback opened a seven-point lead six minutes from time.
Wales lost their home opener to England but having edged out Scotland and now beaten France, they are back in the title battle with top two Ireland and England -- both also on four points -- meeting in Dublin on Sunday. France though are surely out of contention on two.
(Editing by Mark Meadows)
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